Sign Normalised Hammerstein Spline Adaptive Filtering Algorithm in an Impulsive Noise Environment

  • Chang LiuEmail author
  • Zhi Zhang
  • Xiao Tang


In this paper, a sign normalised least mean square algorithm (SNLMS) based on Hammerstein spline adaptive filter (HSAF) is proposed, which is derived by minimising the absolute value of the a posteriori error. The control points, collected in an adaptive lookup table which is interpolated by a local low-order polynomial spline curve and the tap weights of the linear filter are updated by using the direction information of the a posteriori error. The minimization of the absolute value of the a posteriori error reduces the impact of impulsive noises. The new algorithm is called HSAF-SNLMS and can be used to identify the Hammerstein-type nonlinear systems. Furthermore, the convergence performance analysis is carried out by considering the identification of the Hammerstein-type system and the computational complexity of the proposed algorithm is also analyzed. Simulation results in system identification demonstrate the proposed HSAF-SNLMS obtains more robust performance when compared with the existing spline adaptive filter algorithms in impulsive noise environments.


Adaptive filtering Hammerstein spline filter Sign adaptive algorithm 



This research was supported by the National Natural Science Foundation of China under Grant 61501119.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electronic EngineeringDongguan University of TechonologyDong’guanChina

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